Question

During an adiabatic compression of 3 moles of an ideal gas, its temperature increases from 300 K to 400 K. Determine the change of its internal energy during this process. The molar specific heat of the gas at constant volume is 20 joules/mole/K.

(a) 3000 J
(b) 6000 J
(c) 9000 J
(d) 12000 J

Answer 1

The change in internal energy during the adiabatic compression of an ideal gas can be calculated using the formula ΔU = nCvΔT. Given 3 moles of gas, a molar specific heat at constant volume of 20 J/mole/K, and a temperature increase of 100 K, the result is 6000 J.

Step-by-step explanation:

The question asks about the change in internal energy during an adiabatic compression of an ideal gas. For an ideal gas, the change in internal energy (ΔU) can be determined using the molar specific heat at constant volume (Cv) and the change in temperature (ΔT) using the following expression:

ΔU = nCvΔT

Given that n = 3 moles, Cv = 20 J/mole/K, and ΔT = (400 K - 300 K) = 100 K, we can substitute the values into the equation to find the change in internal energy:

ΔU = (3 moles)(20 J/mole/K)(100 K)

ΔU = 6000 J

Therefore, the change in internal energy during the adiabatic compression is 6000 J.